PM2.5 data space-time interpolation method based on space-time Kriging neural network

Abstract

The embodiment of the invention provides a PM2.5 data space-time interpolation method based on a space-time Kriging neural network, and belongs to the technical field of data processing, and the method specifically comprises the steps: collecting space-time monitoring point data; dividing a space-time sampling point set and a non-sampling point set according to the PM2.5 concentration; mapping the attributes of the time-space monitoring points to a high-dimensional space to obtain attribute representation vectors; mapping time and space information to a high-dimensional space to obtain time and space representation vectors; designing a space-time covariance network based on attribute, time and space representation vectors, and fitting covariance matrixes of sampling points and non-sampling points; designing a space-time trend element network to fit a non-stationary space-time trend relationship to obtain a trend characteristic matrix of space-time sampling points and non-sampling points; based on the covariance matrix and the trend characteristic matrix, estimating the PM2.5 concentration of non-sampling points by using a space-time Kriging equation; and optimizing the model and realizing data interpolation prediction. Through the scheme of the invention, the interpolation precision is improved.

Description

Technical Field

[0001] The embodiments of the present invention relate to the technical field of data processing, and in particular, to a spatio-temporal interpolation method for PM2.5 data based on spatio-temporal Kriging neural network. Background Art

[0002] At present, due to limitations of objective factors such as construction costs and environmental conditions, the spatio-temporal monitoring data based on air quality monitoring stations are sparsely and non-uniformly distributed in time and space. Existing mainstream spatio-temporal data interpolation methods expand spatial interpolation methods based on the above spatio-temporal properties, and can be divided into two categories: deterministic spatio-temporal interpolation and geostatistical spatio-temporal interpolation. Deterministic spatio-temporal interpolation methods use pre-defined mathematical and geometric functions, fit the correlation relationships inside the data based on the numerical attributes of spatio-temporal data, and estimate the attribute values of unsampled spatio-temporal points, including spatio-temporal inverse distance weighting, radial basis function method, trend surface method, etc. For example, the trend surface method uses polynomial regression to fit the spatio-temporal sampling point data into a spatio-temporal trend surface function, and then estimates the attribute values of any unsampled spatio-temporal points. Geostatistical spatio-temporal interpolation regards data attributes as random variables under spatio-temporal random processes, couples time and space covariance functions based on the second-order stationary hypothesis, establishes a spatio-temporal covariance function to express spatio-temporal dependence relationships, and thus infers the attribute values of unsampled spatio-temporal points in the form of best linear unbiased estimation. Typical methods include spatio-temporal ordinary Kriging and spatio-temporal simple Kriging. On this basis, improved methods such as spatio-temporal co-Kriging and spatio-temporal universal Kriging consider the influence of multiple factors and the existence of spatio-temporal trends, and are introduced into PM2.5 spatio-temporal interpolation applications to capture multi-factor spatio-temporal dependence and spatio-temporal trend relationships. However, the above methods are all based on certain expert prior knowledge and assumptions, such as pre-defined function forms, linear relationship assumptions, etc., and it is difficult to cope with the PM2.5 spatio-temporal evolution process with complex non-linearity and non-stationarity, resulting in unsatisfactory interpolation accuracy.

[0003] It can be seen that there is an urgent need for a spatio-temporal interpolation method for PM2.5 data based on spatio-temporal Kriging neural network with high interpolation accuracy. Summary of the Invention

[0004] In view of this, the embodiments of the present invention provide a spatio-temporal interpolation method for PM2.5 data based on spatio-temporal Kriging neural network, which at least partially solves the problem of poor interpolation accuracy in the prior art.

[0005] The embodiments of the present invention provide a spatio-temporal interpolation method for PM2.5 data based on spatio-temporal Kriging neural network, including: Step 1, collect data of a total of spatio-temporal monitoring points of air quality monitoring stations in the research area within a preset time range, where each spatio-temporal monitoring point data includes its corresponding spatial information, time information, and attribute characteristics; Step 2, divide the data of spatio-temporal monitoring points into a spatio-temporal sampling point set and a spatio-temporal non-sampling point set according to the PM2.5 concentration monitoring value in the attribute feature; Step 3, design an attribute representation encoder with two network hidden layers, map the attribute features of all spatio-temporal monitoring points to a high-dimensional hidden space, and obtain an attribute representation vector; Step 4, design a time representation encoder and a space representation encoder, map the time information and space information to a high-dimensional hidden space, and obtain a time representation vector and a space representation vector; Step 5, based on the attribute representation vector, time representation vector and space representation vector, design a spatio-temporal covariance network to fit the first spatio-temporal covariance matrix corresponding to the spatio-temporal sampling point set and the second spatio-temporal covariance matrix corresponding to the spatio-temporal non-sampling point set; Step 6, based on the time representation vector and space representation vector, design a spatio-temporal trend element network to fit the non-stationary spatio-temporal trend relationship, and obtain a first spatio-temporal trend feature matrix corresponding to the spatio-temporal sampling point set and a second spatio-temporal trend feature matrix corresponding to the spatio-temporal non-sampling point set; Step 7, based on the first spatio-temporal covariance matrix, second spatio-temporal covariance matrix, first spatio-temporal trend feature matrix and second spatio-temporal trend feature matrix, calculate the PM2.5 concentration estimated value of the spatio-temporal non-sampling point according to the spatio-temporal Kriging equation based on the geostatistical theory; Step 8, divide the spatio-temporal sampling point set into a training set and a validation set according to a preset ratio, calculate the error between the PM2.5 concentration monitoring value and the PM2.5 concentration estimated value in the training set, and take minimizing the error as the goal. Update the learnable parameters in the model in a cyclic iteration manner. When the model achieves the minimum interpolation error in the validation set, obtain the target model to interpolate the data to be processed. According to a specific implementation manner of an embodiment of the present invention, the step 2 specifically includes:

[0006] Judge whether the PM2.5 concentration monitoring value in the attribute feature is a null value. If the PM2.5 concentration monitoring value in the attribute feature is not a null value, then include this spatio-temporal monitoring point into the spatio-temporal sampling point set SP, otherwise include it into the spatio-temporal non-sampling point set UP, and set the corresponding PM2.5 concentration value to 0, where the numbers of spatio-temporal sampling points and spatio-temporal non-sampling points are respectively and , and ; and and .

[0007] According to a specific implementation manner of an embodiment of the present invention, the step 4 specifically includes: Step 4.1, based on the time information of the spatio-temporal monitoring point ​ , calculate the time representation sub-vector towards : ; Among them, ; Step 4.2, splice all the time representation sub-vectors , to obtain the time representation vector : ; Among them, represents the vector splicing operator; Step 4.3, based on the spatio-temporal monitoring point 's spatial information , calculate the corresponding spatial representation sub-vector through different combinations of sine and cosine functions : ; Among them, ; Step 4.4, splice all the spatial representation sub-vectors , to obtain the spatial representation vector : ; Among them, represents the vector splicing operator.

[0008] According to a specific implementation manner of the embodiment of the present invention, the step 5 specifically includes: Step 5.1, project the attribute representation vectors of all spatio-temporal monitoring points, the time representation vector and the spatial representation vector to the time query space and the spatial query space respectively, to obtain the corresponding time query vector and the spatial query vector ; ; Among them, is a network learnable parameter, represents the vector splicing operation operator, represents the weights of the time and spatial representation vectors, used to control the importance degree of spatio-temporal dependence in the spatio-temporal covariance; Step 5.2, the attribute representation vectors of the spatio-temporal sampling point set, the time representation vector , are respectively projected onto the time key space and the space key space to obtain corresponding time key vectors and space key vectors : ; ; wherein, are network learnable parameters; Step 5.3, calculate the time query vector and the similarity of all time key vectors in the high-dimensional space to express the time covariance relationship, and obtain the time covariance vector between the spatio-temporal monitoring point and all spatio-temporal sampling points : ; Step 5.4, calculate the space query vector and the similarity of all space key vectors in the high-dimensional space to express the space covariance relationship, and obtain the space covariance vector between the spatio-temporal monitoring point and all spatio-temporal sampling points : ; Step 5.5, based on the time covariance vector and the space covariance vector of the spatio-temporal monitoring point , perform adaptive mapping through three network layers to obtain the spatio-temporal covariance weight : ; wherein, are network learnable parameters, and the spatio-temporal covariance weight contains three weighted weight values, namely ; Step 5.6, combine the spatio-temporal covariance weighted weight , the time covariance vector and the space covariance vector to obtain the spatio-temporal covariance vector of the spatio-temporal monitoring point : ; wherein, represents the Hadamard product; Step 5.7, extract the spatio-temporal covariance vectors belonging to the set of spatio-temporal unsampled points, and construct the second spatio-temporal covariance matrix corresponding to the unsampled points , while extracting the spatio-temporal covariance vectors belonging to the spatio-temporal sampling point set, and constructing the first spatio-temporal covariance matrix corresponding to the spatio-temporal sampling point set , and setting the diagonal elements of the first spatio-temporal covariance matrix to 0.

[0009] According to a specific implementation manner of an embodiment of the present invention, the step 6 specifically includes: Step 6.1, taking the spatial representation vector and the temporal representation vector of each spatio-temporal monitoring point as meta-knowledge, and obtaining the spatio-temporal trend mapping weight through a meta-learner: ; ; wherein, represents the learnable parameters of the meta-learner; Step 6.2, based on the spatio-temporal trend mapping weight, mapping the time and spatial positions of each spatio-temporal monitoring point to a spatio-temporal trend feature vector : ; wherein, is the spatio-temporal trend mapping weight obtained in step 6.1, represents the dimension size of the spatio-temporal trend feature vector; Step 6.3, respectively extracting the spatio-temporal trend vectors of the spatio-temporal sampling point set and the spatio-temporal non-sampling point set, and constructing the first spatio-temporal trend feature matrix corresponding to the spatio-temporal sampling point set, and the second spatio-temporal trend feature matrix corresponding to the spatio-temporal non-sampling point set.

[0010] According to a specific implementation manner of an embodiment of the present invention, the step 7 specifically includes: Step 7.1, for each spatio-temporal non-sampling point constructing a spatio-temporal Kriging equation, and solving the spatio-temporal interpolation weight corresponding to the spatio-temporal non-sampling point: ; wherein, is the Lagrange term coefficient, represents the vector composed of the th row elements in the second spatio-temporal covariance matrix, that is, the spatio-temporal covariance vector corresponding to the spatio-temporal non-sampling point ; represents the second spatio-temporal trend feature matrix Middle A vector of row elements, i.e., unsampled points in time and space The corresponding spatiotemporal trend feature vector; Step 7.2, according to the spatiotemporal interpolation weight , based on the vector of PM2.5 concentration monitoring values at all spatiotemporal sampling points , calculate the unsampled points in time and space Estimated PM2.5 concentration : .

[0011] According to a specific implementation of the embodiment of the present invention, step 8 specifically includes: Step 8.1, calculate the root mean square error as the loss function of model training based on the error between the PM2.5 concentration monitoring value and the PM2.5 concentration estimation value in the training set, where the expression of the loss function is: ; in, Indicates the PM2.5 concentration monitoring value, Represents the number of spatiotemporal monitoring points in the training set; Step 8.2, use the back propagation algorithm to calculate the loss each time All learnable parameters in the model are passed to it, and the Adam optimization strategy is used to iteratively update each learnable parameter based on the gradient of the returned loss until the model reaches the minimum interpolation error in the validation set and the target model is obtained; In step 8.3, the target model is used to interpolate the data to be processed.

[0012] The PM2.5 data spatiotemporal interpolation scheme based on spatiotemporal Kriging neural network in the embodiment of the present invention comprises: step 1, collecting the total PM2.5 data from air quality monitoring stations in the study area within a preset time range; spatiotemporal monitoring point data, wherein each spatiotemporal monitoring point data includes its corresponding spatial information, time information and attribute characteristics; step 2, according to the PM2.5 concentration monitoring value in the attribute characteristics, Divide the data of each spatio-temporal monitoring point into a spatio-temporal sampling point set and a spatio-temporal unsampled point set; Step 3, design an attribute representation encoder with two network hidden layers to map the attribute features of all spatio-temporal monitoring points to a high-dimensional hidden space to obtain attribute representation vectors; Step 4, design a time representation encoder and a space representation encoder to map time information and space information to a high-dimensional hidden space to obtain a time representation vector and a space representation vector; Step 5, based on the attribute representation vector, the time representation vector and the space representation vector, design a spatio-temporal covariance network to fit the first spatio-temporal covariance matrix corresponding to the spatio-temporal sampling point set and the second spatio-temporal covariance matrix corresponding to the spatio-temporal unsampled point set; Step 6, based on the time representation vector and the space representation vector, design a spatio-temporal trend element network to fit the non-stationary spatio-temporal trend relationship to obtain the first spatio-temporal trend feature matrix corresponding to the spatio-temporal sampling point set and the second spatio-temporal trend feature matrix corresponding to the spatio-temporal unsampled point set; Step 7, based on the first spatio-temporal covariance matrix, the second spatio-temporal covariance matrix, the first spatio-temporal trend feature matrix and the second spatio-temporal trend feature matrix, calculate the PM2.5 concentration estimated value of the spatio-temporal unsampled point according to the spatio-temporal Kriging equation based on geostatistical theory; Step 8, divide the spatio-temporal sampling point set into a training set and a validation set according to a preset ratio, calculate the error between the PM2.5 concentration monitoring value and the PM2.5 concentration estimated value in the training set, and take minimizing the error as the goal, and update the learnable parameters in the model in a cyclic iterative manner. When the model achieves the minimum interpolation error in the validation set, obtain the target model to perform interpolation on the data to be processed.

[0013] The beneficial effects of the embodiments of the present invention are as follows: Through the solution of the present invention, design time, space representation encoders and a spatio-temporal covariance network, and in the high-dimensional hidden space, adaptively map and couple the spatio-temporal covariance of multi-factor potential influences and complex spatio-temporal dependencies, and model the non-linear multi-variable spatio-temporal dependence relationship; design a spatio-temporal trend element network, and accurately capture and fit the dynamic process of the PM2.5 spatio-temporal evolution trend based on the idea of meta-learning, and model the non-stationary spatio-temporal trend relationship; based on the spatio-temporal Kriging method, comprehensively express the multi-variable spatio-temporal dependence and non-stationary spatio-temporal trend relationship, and use the backpropagation process of deep learning to adaptively adjust the network parameters to achieve a high-precision and intelligent spatio-temporal interpolation process. Description of the Drawings

[0014] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required to be used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained according to these drawings.

[0015] Figure 1Schematic flow chart of a PM2.5 data spatio-temporal interpolation method based on spatio-temporal Kriging neural network provided by an embodiment of the present invention; Figure 2 Schematic diagram of the specific implementation process of a PM2.5 data spatio-temporal interpolation method based on spatio-temporal Kriging neural network provided by an embodiment of the present invention; Figure 3 Spatial distribution map of the average error of different spatio-temporal interpolation methods provided by an embodiment of the present invention. Detailed implementation manners

[0016] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0017] The following uses specific specific examples to illustrate the implementation manners of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. The present invention can also be implemented or applied through other different specific implementation manners. Various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, without conflict, the following embodiments and the features in the embodiments can be combined with each other. Based on the embodiments in the present invention, all other embodiments obtained by those of ordinary skill in the art without making creative efforts belong to the scope of protection of the present invention.

[0018] It should be noted that the following describes various aspects of the embodiments within the scope of the appended claims. It should be obvious that the aspects described herein can be embodied in a wide variety of forms, and any specific structure and / or function described herein is illustrative only. Based on the present invention, those skilled in the art should understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects described herein can be used to implement the device and / or practice the method. In addition, this device and / or practice this method can be implemented using other structures and / or functions in addition to one or more of the aspects described herein.

[0019] It should also be noted that the diagrams provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner. The diagrams only show the components related to the present invention, rather than being drawn according to the number, shape and size of the components in actual implementation. The type, quantity and proportion of each component in its actual implementation can be an arbitrary change, and the component layout type may also be more complex.

[0020] In addition, in the following description, specific details are provided to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that the described aspects can be practiced without these specific details.

[0021] Due to limitations of objective factors such as construction costs and environmental conditions, the spatio-temporal monitoring data based on air quality monitoring stations shows sparse and non-uniform distribution in terms of time and space. Therefore, how to design an accurate spatio-temporal interpolation method for PM2.5 data, model the inherent spatio-temporal evolution law of PM2.5 based on the known spatio-temporal sampling point data, and thus infer the PM2.5 concentration values at unsampled spatio-temporal points is the key to achieving urban sustainable development and improving the happiness index of residents.

[0022] There is a certain systematicity, i.e., spatio-temporal trend, in the dynamic evolution process of the spatio-temporal distribution of PM2.5. Accurately capturing and fitting this dynamically changing spatio-temporal trend is the underlying goal of the spatio-temporal interpolation model. At the same time, due to the cross-influence of other atmospheric particles, wind speed and other confounding factors on the spatio-temporal evolution process of PM2.5, corresponding random fluctuations are also shown on the basis of the spatio-temporal trend. Moreover, the spatio-temporal distribution of PM2.5 conforms to spatio-temporal dependence, that is, the PM2.5 concentration values in spatio-temporal proximity are closer. Therefore, how to fit and couple the complex multivariate spatio-temporal dependence relationship and spatio-temporal trend relationship is the key to guiding the design of a high-precision spatio-temporal interpolation model for PM2.5 data.

[0023] The existing mainstream spatio-temporal data interpolation methods extend the spatial interpolation methods based on the above spatio-temporal properties and can be divided into two categories: deterministic spatio-temporal interpolation and geostatistical spatio-temporal interpolation. The deterministic spatio-temporal interpolation method uses a pre-defined mathematical geometric function to fit the correlation relationship inside the data based on the numerical attributes of the spatio-temporal data and estimates the attribute values of unsampled spatio-temporal points, including spatio-temporal inverse distance weighting, radial basis function method, trend surface method, etc. For example, the trend surface method uses polynomial regression to fit the spatio-temporal sampling point data into a spatio-temporal trend surface function, and then estimates the attribute values of any unsampled spatio-temporal points. Geostatistical spatio-temporal interpolation regards the data attributes as random variables under the spatio-temporal random process, couples the time and space covariance functions based on the second-order stationary hypothesis, establishes a spatio-temporal covariance function to express the spatio-temporal dependence relationship, and thus infers the attribute values of unsampled spatio-temporal points in the way of best linear unbiased estimation. Typical methods include spatio-temporal ordinary Kriging and spatio-temporal simple Kriging. On this basis, improved methods such as spatio-temporal co-Kriging and spatio-temporal universal Kriging consider the influence of multiple factors and the existence of spatio-temporal trends and are introduced into the PM2.5 spatio-temporal interpolation application to capture the multivariate spatio-temporal dependence and spatio-temporal trend relationship. However, the above methods are all based on certain expert prior knowledge and assumptions, such as pre-defined function forms, linear relationship assumptions, etc., and are difficult to cope with the PM2.5 spatio-temporal evolution process with complex non-linearity and non-stationarity coexisting, resulting in unsatisfactory interpolation accuracy.

[0024] In recent years, with the rapid development of deep learning technology and its mature applications in various industries, various deep learning models have also been applied to address the challenges of accurate spatio-temporal interpolation of PM2.5, such as recurrent neural networks, graph neural networks, attention networks, and meta-learning networks. However, these methods often can only handle a single challenge, such as the non-linear problem of multivariate spatio-temporal dependence or the non-stationary problem of spatio-temporal trends, and cannot comprehensively consider the two in a unified framework, resulting in insufficient information utilization and limited accuracy of the interpolation results.

[0025] An embodiment of the present invention provides a spatio-temporal interpolation method for PM2.5 data based on spatio-temporal Kriging neural network, and the method can be applied to the process of air pollution prevention and control in the environmental protection scenario.

[0026] See Figure 1 , which is a schematic flow chart of a spatio-temporal interpolation method for PM2.5 data based on spatio-temporal Kriging neural network provided by an embodiment of the present invention. As Figure 1 and Figure 2 shown, the method mainly includes the following steps: Step 1, collect data of a total of spatio-temporal monitoring points of air quality monitoring stations in the research area within a preset time range, where each spatio-temporal monitoring point data includes its corresponding spatial information, time information, and attribute characteristics; The PM2.5 data used in this implementation plan comes from the hourly monitoring data of 19 air quality monitoring stations in City A provided by the national urban air quality real-time release platform from March 1, 2021 to March 7, 2021. It includes the PM2.5 concentration monitoring value as the interpolation target and other relevant monitoring covariates (PM10, SO2, NO2, O3, CO). After data cleaning, a total of 3108 valid data of spatio-temporal monitoring points are included to illustrate the implementation process of the present invention.

[0027] Specifically, when implementing, collect data of a total of spatio-temporal monitoring points of air quality monitoring stations in the research area within a certain time range , and a single spatio-temporal monitoring point includes the site spatial location information , time information , and attribute characteristics . Among them, the attribute characteristics include multiple monitoring attributes related to PM2.5, represents the PM2.5 concentration monitoring value, represents covariates.

[0028] Step 2: Divide the data of spatio-temporal monitoring points into a spatio-temporal sampling point set and a spatio-temporal non-sampling point set according to the PM2.5 concentration monitoring value within the attribute features; Specifically, it can be determined whether the attribute feature is a null value. If the PM2.5 concentration monitoring value within the attribute feature is not a null value, then include this spatio-temporal monitoring point in the spatio-temporal sampling point set SP; otherwise, include it in the spatio-temporal non-sampling point set NP and set the corresponding PM2.5 concentration value to 0. Among them, the numbers of spatio-temporal sampling points and spatio-temporal non-sampling points are respectively and and , and .

[0029] Step 3: Design an attribute representation encoder with two network hidden layers to map the attribute features of all spatio-temporal monitoring points to a high-dimensional hidden space to obtain an attribute representation vector; Specifically, design an attribute representation encoder with two network hidden layers to map the attribute features of all spatio-temporal monitoring points to a high-dimensional hidden space to obtain an attribute representation vector : ; Among them, are network learnable parameters, is a non-linear activation function, represents the dimension size of the high-dimensional hidden space.

[0030] Step 4: Design a time representation encoder and a space representation encoder to map time information and space information to a high-dimensional hidden space to obtain a time representation vector and a space representation vector; Specifically, for the time information and space information of each spatio-temporal monitoring point , respectively design a time representation encoder and a space representation encoder to map the low-dimensional time and space information to a high-dimensional hidden space to obtain a time representation vector and a space representation vector . It mainly includes the following steps: Based on the time information of the spatio-temporal monitoring point, calculate the corresponding time representation sub-vector through the sine function and cosine function: ; Among them, .

[0031] Furthermore, concatenate all the time representation sub-vectors , obtain the corresponding time representation vector : ; Among them, represents the vector concatenation operator.

[0032] Based on the spatial position information of the spatio-temporal monitoring points , calculate the corresponding spatial representation sub-vectors through different combinations of sine and cosine functions : ; Among them, .

[0033] Furthermore, concatenate all the spatial representation sub-vectors , and obtain the corresponding spatial representation vector : ; Among them, represents the vector concatenation operator. Based on the properties of sine and cosine functions, the dot product results of the time representation vectors will gradually decay as the time distance increases, thereby expressing the time dependence relationship; similarly, the dot product results of the spatial representation vectors will gradually decay as the spatial distance increases, thereby expressing the spatial dependence relationship.

[0034] Step 5, based on the attribute representation vector, time representation vector and spatial representation vector, design a spatio-temporal covariance network to fit the first spatio-temporal covariance matrix corresponding to the spatio-temporal sampling point set and the second spatio-temporal covariance matrix corresponding to the spatio-temporal non-sampling point set; In specific implementation, based on the attribute representation vector and the time representation vector and the spatial representation vector , design a spatio-temporal covariance network to fit the spatio-temporal covariance matrix between spatio-temporal monitoring points and spatio-temporal sampling points: specifically including the spatio-temporal covariance matrix of spatio-temporal sampling points, and the spatio-temporal covariance matrix of spatio-temporal non-sampling points, including the following steps.

[0035] Extract the attribute representation vectors , time representation vectors and spatial representation vectors of all spatio-temporal monitoring points, project them into the time query space and spatial query space respectively, and obtain the corresponding time query vectors and spatial query vectors , and the formula is as follows: ; ; Among them, are network learnable parameters, represents the vector concatenation operator, represents the weights of the temporal and spatial representation vectors, and is used to control the importance degree of the spatio-temporal dependence in the spatio-temporal covariance.

[0036] Extract the attribute representation vector belonging to the spatio-temporal sampling point set , the temporal representation vector and the spatial representation vector , and project them into the temporal key space and the spatial key space respectively to obtain the corresponding temporal key vector and the spatial key vector , and the formula is as follows: ; ; Among them, are network learnable parameters.

[0037] Calculate the similarity between the temporal query vector and all temporal key vectors in the high-dimensional space, express the temporal covariance relationship, and obtain the spatio-temporal covariance vector between the spatio-temporal monitoring point and all spatio-temporal sampling points, and the specific formula is as follows: ; Calculate the similarity between the spatial query vector and all spatial key vectors in the high-dimensional space, express the spatial covariance relationship, and obtain the spatio-temporal covariance vector between the spatio-temporal monitoring point and all spatio-temporal sampling points, and the specific formula is as follows: ; Based on the temporal covariance vector of the spatio-temporal monitoring point and the spatial covariance vector , perform adaptive mapping through three network layers to obtain the spatio-temporal covariance weight , and the specific formula is as follows: ; Among them, are network learnable parameters, and the spatio-temporal covariance weight contains three weighted weight values, that is, .

[0038] Combine the spatio-temporal covariance weighted weight with the spatial and temporal covariance vectors , spatio-temporal monitoring points are obtained of the spatio-temporal covariance vector : ; Among them, represents the Hadamard product.

[0039] Extract the spatio-temporal covariance vectors belonging to the set of spatio-temporal unsampled points, and construct the spatio-temporal covariance matrix of the unsampled points ; At the same time, extract the spatio-temporal covariance vectors belonging to the set of spatio-temporal sampled points, and construct the spatio-temporal covariance matrix of the sampled points . Among them, to avoid the influence of its own information, the diagonal elements of the matrix are set to 0.

[0040] Step 6, based on the time representation vector and the space representation vector, design a spatio-temporal trend element network to fit the non-stationary spatio-temporal trend relationship, and obtain the first spatio-temporal trend feature matrix corresponding to the set of spatio-temporal sampled points and the second spatio-temporal trend feature matrix corresponding to the set of spatio-temporal unsampled points; Specifically, based on the space representation vector and the time representation vector , design a spatio-temporal trend element network to fit the non-stationary spatio-temporal trend relationship. The specific steps are as follows: Take the space representation vector and the time representation vector of each spatio-temporal monitoring point as meta-knowledge, and obtain the spatio-temporal trend mapping weight through the meta-learner. The specific formula is as follows: ; ; Among them, represents the learnable parameters of the meta-learner.

[0041] Based on the spatio-temporal trend mapping weight, map the time and space positions of each spatio-temporal monitoring point to the spatio-temporal trend feature vector . The calculation formula is as follows: ; Among them, is the spatio-temporal trend mapping weight obtained in Step 6.1, represents the dimension size of the spatio-temporal trend feature vector.

[0042] Extract the spatio-temporal trend vectors of the spatio-temporal sampled points and the unsampled ones respectively, and form the spatio-temporal trend feature matrix of the unsampled points , and the spatio-temporal trend feature matrix of the sampled points .

[0043] Step 7: Based on the first spatio-temporal covariance matrix, the second spatio-temporal covariance matrix, the first spatio-temporal trend feature matrix, and the second spatio-temporal trend feature matrix, calculate the estimated PM2.5 concentration value of the spatio-temporal unsampled points according to the spatio-temporal Kriging equation based on geostatistical theory; In specific implementation, based on the spatio-temporal covariance matrix and the spatio-temporal trend feature matrix , according to the spatio-temporal Kriging equation based on geostatistical theory, comprehensively considering the above two types of spatio-temporal relationships, calculate the estimated PM2.5 concentration value of the spatio-temporal unsampled points , including the following steps.

[0044] For each spatio-temporal unsampled point Construct a spatio-temporal Kriging equation and solve the spatio-temporal interpolation weights corresponding to the spatio-temporal unsampled point , and the specific formula is: ; where is the Lagrange term coefficient, represents the vector composed of the elements in the th row of the spatio-temporal covariance matrix , that is, the spatio-temporal covariance vector corresponding to the spatio-temporal unsampled point ; represents the vector composed of the elements in the th row of the spatio-temporal trend feature matrix , that is, the spatio-temporal trend feature vector corresponding to the spatio-temporal unsampled point .

[0045] According to the spatio-temporal interpolation weights , based on the vector formed by the PM2.5 concentration values of all spatio-temporal sampled points, calculate the estimated PM2.5 concentration value of the spatio-temporal unsampled point : .

[0046] Step 8: Divide the spatio-temporal sampled point set into a training set and a validation set according to a preset ratio, calculate the error between the monitored PM2.5 concentration value and the estimated PM2.5 concentration value in the training set, and take minimizing the error as the goal. Update the learnable parameters in the model through iterative cycles. When the model achieves the minimum interpolation error in the validation set, obtain the target model to interpolate the data to be processed.

[0047] In specific implementation, 80% of the spatio-temporal sampled points are used as the training set, and the remaining 20% are used as the validation set. Calculate the true value of the PM2.5 concentration The error between the model estimated values and aims to minimize the error, thereby continuously updating the learnable parameters in the model through iterative loops, ultimately enabling the model to achieve the minimum interpolation error in the validation set. Specifically, it includes the following steps: Adopt the root mean square error as the model training loss function, and the specific formula is: ; Among them, and respectively represent the model estimated value and the true value of the PM2.5 concentration in the training set, represents the number of spatio-temporal monitoring points in the training set.

[0048] Use the backpropagation algorithm to pass the loss calculated each time to all the learnable parameters in the model. At the same time, adopt the Adam optimization strategy to iteratively update each learnable parameter based on the gradient of the returned loss until the model reaches the lowest interpolation error in the validation set.

[0049] Finally, the trained target model can be used for actual high-precision spatio-temporal interpolation applications.

[0050] Adopt existing multi-type spatio-temporal interpolation methods to conduct experimental comparisons with the present invention to test the effectiveness of the method proposed by the present invention. The selected comparison methods include: spatio-temporal inverse distance weighting (STIDW), spatio-temporal ordinary kriging (STOK), and geographical-time neural network weighted regression method (GTNNWR).

[0051] Randomly select 60% of all spatio-temporal monitoring points in the dataset as the spatio-temporal unsampled point set, and the rest are included in the spatio-temporal sampled point set. Based on the spatio-temporal sampled point set, construct and train the model, estimate the PM2.5 concentration values of the spatio-temporal unsampled points, and quantitatively evaluate the spatio-temporal interpolation results using multiple precision evaluation indicators, including ① mean absolute error (MAE); ② root mean square error (RMSE); ③ mean absolute percentage error (MAPE), and the calculation formulas are as follows: ; ; ; Among them, and respectively represent the true value and the model estimated value of the PM2.5 concentration at the th spatio-temporal unsampled point, represents the number of spatio-temporal unsampled points. For the above three evaluation indicators, the smaller the value of the indicator, the higher the precision of the spatio-temporal interpolation method.

[0052] Table 1 shows the accuracy comparison results between the method of the present invention and the comparative method on the PM2.5 dataset. It can be found that the method of the present invention is superior to the comparative method in all three evaluation indicators, indicating that the method of the present invention has achieved the best accuracy performance overall.

[0053] Table 1 ; Based on the interpolation results of the method of the present invention and the comparative method, the absolute value of the PM2.5 spatio-temporal interpolation error is averaged according to the spatial positions of the spatio-temporal unsampled points and spatially visualized, as Figure 3 shown. Among them, (a) represents the method of the present invention, and (b), (c), and (d) are existing comparative methods. It can be found that compared with the comparative method, the average error of the method of the present invention is relatively smaller and more evenly distributed in space, indicating that the method of the present invention can effectively improve the stability of spatio-temporal interpolation.

[0054] The PM2.5 data spatio-temporal interpolation method based on spatio-temporal Kriging neural network provided in this embodiment designs a time and space feature encoder and a spatio-temporal covariance network, and adaptively maps and couples the spatio-temporal covariance of multi-factor potential influences and complex spatio-temporal dependencies in a high-dimensional hidden space to model non-linear multi-variable spatio-temporal dependence relationships; designs a spatio-temporal trend meta-network to accurately capture and fit the dynamic process of the PM2.5 spatio-temporal evolution trend based on the idea of meta-learning, and models non-stationary spatio-temporal trend relationships; based on the spatio-temporal Kriging method, comprehensively expresses multi-variable spatio-temporal dependence and non-stationary spatio-temporal trend relationships, and adaptively adjusts network parameters using the backpropagation process of deep learning to achieve a high-precision and intelligent spatio-temporal interpolation process.

[0055] It should be understood that each part of the present invention can be implemented by hardware, software, firmware, or a combination thereof.

[0056] The above is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present invention should be covered by the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims

1. A spatio-temporal interpolation method for PM2.5 data based on spatio-temporal Kriging neural network, characterized in that, Including: Step 1, collect data of a total of spatiotemporal monitoring points of air quality monitoring stations within the research area during the preset time range. Among them, the data of each spatiotemporal monitoring point includes its corresponding spatial information, time information, and attribute characteristics; Step 2, divide the data of spatiotemporal monitoring points into a spatiotemporal sampling point set and a spatiotemporal non-sampling point set according to the PM2.5 concentration monitoring value within the attribute characteristics; Step 3: Design an attribute representation encoder with two network hidden layers to map the attribute features of all spatio-temporal monitoring points to a high-dimensional hidden space, and obtain an attribute representation vector; Step 4: Design a time representation encoder and a space representation encoder to map time information and space information to a high-dimensional hidden space, and obtain a time representation vector and a space representation vector; Step 5: Based on the attribute representation vector, the time representation vector, and the space representation vector, design a spatio-temporal covariance network to fit the first spatio-temporal covariance matrix corresponding to the spatio-temporal sampling point set and the second spatio-temporal covariance matrix corresponding to the spatio-temporal unsampled point set; Step 6: Based on the time representation vector and the space representation vector, design a spatio-temporal trend element network to fit the non-stationary spatio-temporal trend relationship, and obtain the first spatio-temporal trend feature matrix corresponding to the spatio-temporal sampling point set and the second spatio-temporal trend feature matrix corresponding to the spatio-temporal unsampled point set; Step 7: Based on the first spatio-temporal covariance matrix, the second spatio-temporal covariance matrix, the first spatio-temporal trend feature matrix, and the second spatio-temporal trend feature matrix, calculate the PM2.5 concentration estimated value of the spatio-temporal unsampled point according to the spatio-temporal Kriging equation based on geostatistical theory; Step 8: Divide the spatio-temporal sampling point set into a training set and a validation set according to a preset ratio, calculate the error between the PM2.5 concentration monitoring value and the PM2.5 concentration estimated value in the training set, and take minimizing the error as the goal. Update the learnable parameters in the model in a cyclic iterative manner. When the model achieves the minimum interpolation error in the validation set, obtain the target model to interpolate the data to be processed.

2. The method according to claim 1, wherein The specific content of step 2 includes: Determine the attribute characteristics Whether the PM2.5 concentration monitoring value within is a null value. If the attribute characteristics The PM2.5 concentration monitoring value within is not a null value, then include this spatio-temporal monitoring point Into the spatio-temporal sampling point set SP, otherwise into the spatio-temporal non-sampled point set UP, and set the corresponding PM2.5 concentration value to 0. Among them, the numbers of spatio-temporal sampling points and spatio-temporal non-sampled points are respectively And , and .

3. The method according to claim 2, wherein The specific content of step 4 includes: Step 4.1, based on the spatio-temporal monitoring points ' time information , calculate the time representation sub-vector through sine and cosine functions : Among them, ; Step 4.2, concatenate all the time representation sub-vectors , to obtain the time representation vector : Among them, represents a vector concatenation operator; Step 4.3, based on the spatio-temporal monitoring points of the spatial information , calculate the corresponding spatial representation sub-vectors through different combinations of sine and cosine functions : Among them, ; Step 4.4, concatenate all the spatial representation sub-vectors , to obtain the spatial representation vector : Among them, represents a vector concatenation operator.

4. The method according to claim 3, characterized in that, The specific content of step 5 includes: Step 5.1, project the attribute representation vectors , time representation vectors and spatial representation vectors into the time query space and the spatial query space respectively to obtain the corresponding time query vectors and spatial query vectors : Among them, are network learnable parameters, represents a vector concatenation operator, represents the weights of the temporal and spatial representation vectors, which are used to control the importance of the spatio-temporal dependence in the spatio-temporal covariance; Step 5.2, the attribute characterization vector of the spatio-temporal sampling point set , the time characterization vector , and the space characterization vector are respectively projected onto the time key space and the space key space to obtain the corresponding time key vector and the space key vector : Among them, are network learnable parameters; Step 5.3, calculate the time query vector with all the time key vectors in the high-dimensional space to express the time covariance relationship, and obtain the spatio-temporal monitoring points and the time covariance vectors between all spatio-temporal sampling points : ； Step 5.4, calculate the spatial query vector and all spatial key vectors in the high-dimensional space to express the spatial covariance relationship, and obtain the spatial covariance vectors between all spatio-temporal monitoring points : ； Step 5.5, based on the spatio-temporal monitoring points of the temporal covariance vector and the spatial covariance vector , perform adaptive mapping through three network layers to obtain the spatio-temporal covariance weight : Among them, is a network learnable parameter, the spatio-temporal covariance weight contains three weighted weight values, namely ; Step 5.6, combining the spatio-temporal covariance weighted weights , the time covariance vector and the spatial covariance vector to obtain the spatio-temporal covariance vector of the spatio-temporal monitoring point : Among them, represents the Hadamard product; Step 5.7, extract the spatio-temporal covariance vectors belonging to the spatio-temporal unsampled point set, and construct the second spatio-temporal covariance matrix corresponding to the unsampled points , and at the same time, extract the spatio-temporal covariance vectors belonging to the spatio-temporal sampled point set, and construct the first spatio-temporal covariance matrix corresponding to the spatio-temporal sampled point set , and set the diagonal elements of the first spatio-temporal covariance matrix to 0.

5. The method according to claim 4, wherein The specific content of step 6 includes: Step 6.1, use the spatial representation vector of each spatio-temporal monitoring point and the temporal representation vector as meta-knowledge, and obtain the spatio-temporal trend mapping weight through a meta-learner: Among them, represents the learnable parameters of the meta-learner; Step 6.2, based on the spatio-temporal trend mapping weights, map the time and spatial location of each spatio-temporal monitoring point into a spatio-temporal trend feature vector : ​ Among them, is the spatio-temporal trend mapping weight obtained in step 6.1, indicating the dimension size of the spatio-temporal trend feature vector; Step 6.3: Extract the spatio-temporal trend vectors of the spatio-temporal sampled point set and the spatio-temporal unsampled point set respectively, and form the first spatio-temporal trend feature matrix corresponding to the spatio-temporal sampled point set , and the second spatio-temporal trend feature matrix corresponding to the spatio-temporal unsampled point set .

6. The method according to claim 5, wherein The specific content of step 7 includes: Step 7.1, for each unsampled spatio-temporal point Construct a spatio-temporal Kriging equation and solve for the spatio-temporal interpolation weights corresponding to the unsampled spatio-temporal point : Among them, is the Lagrangian term coefficient, represents the vector composed of the elements in the th row of the second spatio-temporal covariance matrix, that is, the spatio-temporal covariance vector corresponding to the spatio-temporal unsampled point ; represents the vector composed of the elements in the th row of the second spatio-temporal trend feature matrix, that is, the spatio-temporal trend feature vector corresponding to the spatio-temporal unsampled point ; Step 7.2, according to the spatio-temporal interpolation weight , based on the vector formed by the PM2.5 concentration monitoring values of all spatio-temporal sampling points , calculate the PM2.5 concentration estimated value of the spatio-temporal unsampled points : : 。 7. The method according to claim 6, wherein The specific content of step 8 includes: Step 8.1: Calculate the root mean square error as the loss function for model training according to the error between the PM2.5 concentration monitoring value and the PM2.5 concentration estimated value in the training set. Among them, the expression of the loss function is Among them, represents the monitoring value of PM2.5 concentration, represents the number of spatio-temporal monitoring points in the training set; Step 8.2, use the back propagation algorithm to calculate the loss each time All learnable parameters in the model are passed to it, and the Adam optimization strategy is used to iteratively update each learnable parameter based on the gradient of the returned loss until the model reaches the minimum interpolation error in the validation set and the target model is obtained; Step 8.3: Use the target model to interpolate the data to be processed.

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